Take Home Exercise 1

Author

Hao Xian

Published

January 30, 2023

Modified

February 11, 2023

Overview

Setting the Scene

Important

This context is taken from the IS415 Take Home Exercise 1

All rights belong to Dr Kam Tin Seong.

Water is an important resource to mankind. Clean and accessible water is critical to human health. It provides a healthy environment, a sustainable economy, reduces poverty and ensures peace and security. Yet over 40% of the global population does not have access to sufficient clean water. By 2025, 1.8 billion people will be living in countries or regions with absolute water scarcity, according to UN-Water. The lack of water poses a major threat to several sectors, including food security. Agriculture uses about 70% of the world’s accessible freshwater.

Developing countries are most affected by water shortages and poor water quality. Up to 80% of illnesses in the developing world are linked to inadequate water and sanitation. Despite technological advancement, providing clean water to the rural community is still a major development issues in many countries globally, especially countries in the Africa continent.

To address the issue of providing clean and sustainable water supply to the rural community, a global Water Point Data Exchange (WPdx) project has been initiated. The main aim of this initiative is to collect water point related data from rural areas at the water point or small water scheme level and share the data via WPdx Data Repository, a cloud-based data library. What is so special of this project is that data are collected based on WPDx Data Standard.

Objectives

Important

This Objectives are taken from the IS415 Take Home Exercise 1

All rights belong to Dr Kam Tin Seong.

Exploratory Spatial Data Analysis

Derive kernel density maps of functional and non-functional water points. Using appropriate tmap functions,
Display the kernel density maps on openstreetmap of Osub State, Nigeria.
Describe the spatial patterns revealed by the kernel density maps. Highlight the advantage of kernel density map over point map.

Second-Order Spatial Point Patterns Analysis

With reference to the spatial point patterns observed in ESDA:

Formulate the null hypothesis and alternative hypothesis and select the confidence level.
Perform the test by using appropriate Second order spatial point patterns analysis technique.
With reference to the analysis results, draw statistical conclusions.

Spatial Correlation Analysis

In this section, you are required to confirm statistically if the spatial distribution of functional and non-functional water points are independent from each other.

Formulate the null hypothesis and alternative hypothesis and select the confidence level.
Perform the test by using appropriate Second order spatial point patterns analysis technique.
With reference to the analysis results, draw statistical conclusions.

Setup

Packages

sf: used for importing, managing, and processing geospatial data
tidyverse: for performing data science tasks such as importing, wrangling and visualising data.
tmap: used for creating thematic maps, such as choropleth and bubble maps
spatstat: used for point pattern analysis
raster: reads, writes, manipulates, analyses and models gridded spatial data (i.e. raster-based geographical data)
maptools: a set of tools for manipulating geographic data
funModeling: contains a set of functions related to exploratory data analysis, data preparation, and model performance

Installing and Loading the Packages

The code chunk below will be used to install and load these packages in RStudio.

pacman::p_load(maptools, sf, raster, spatstat, tmap, tidyverse, funModeling)

This prepares all the tools necessary for us to start or spatial analysis.

Dataset used

2 datasets are used for this excercise

The First Dataset used would be the Level 2 Administrative Boundary which can be found either from Geoboundaries or Humanitarian Data Exchange
Waterpoint Data Repositories is the dataset for the waterpoint

Handling the Geospatial Data

Importing Geospatial Dataframe

Note

Need to double check the CRS as it is depending on the system used by the country.

Since the country we are focusing on is Nigeria. The EPSG code is 26392., and it encompasses the entire area of Nigeria.

We will be using the st_read() function from the sf package to read the data set. More information on st_read() can be found here..

However, as the polygon data is not in the correct format, there will be a need to convert the geometric data to the correct form. st_transform from the sf package is used to so. More information on st_transform() can be found here

geoBoundaries data set

This dataset loads the boundaries of Nigeria from geoBoundaries

geoNGA <- st_read("data/geospatial/",
                  layer = "geoBoundaries-NGA-ADM2") %>%
  st_transform(crs = 26392)

Reading layer `geoBoundaries-NGA-ADM2' from data source 
  `C:\hxchen-2019\birdie\lessons\Take-home\Take-home_ex1\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 774 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2.668534 ymin: 4.273007 xmax: 14.67882 ymax: 13.89442
Geodetic CRS:  WGS 84

geoNGA contains the following data:

Columns Name	Description
shapeName	Name of the Level 2 Boundaries
pcode	Unique Code
level	ADM2 (Indicating this is a Level 2 Boundaries)
shapeID	Unique Code of the Shape
shapeGroup	NGA (Indicating Nigeria)
shapeType	ADM2 (Indicating this is a Level 2 Boundaries)
geometry	Polygon Data

NGA Data set (Humanitarian Data Exchange)

Note

The NGA Dataset is essentially the same as geoBoundaries dataset with the exception that the dataset in geoBoundaries is more condense.

NGA <- st_read("data/geospatial/",
               layer = "nga_admbnda_adm2_osgof_20190417") %>%
  st_transform(crs = 26392)

Reading layer `nga_admbnda_adm2_osgof_20190417' from data source 
  `C:\hxchen-2019\birdie\lessons\Take-home\Take-home_ex1\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 774 features and 16 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2.668534 ymin: 4.273007 xmax: 14.67882 ymax: 13.89442
Geodetic CRS:  WGS 84

NGA contains the following data:

Column Name	Description
Shape_Leng	Length of the Shape
Shape_Area	Area of the Shape
ADM2_EN	English Name of ADM2
ADM2_PCODE	Unique ID of the ADM2
ADM2_REF	A Reference to ADM2_EN
ADM2ALT1EN	Alternative English Name
ADM2ALT2EN	Alternative English Name
ADM1_EN	ADM1 English Name
ADM1_PCODE	Unique ID of ADM1
ADM0_EN	ADM0 English Name
ADM0_PCODE	Unique ID of ADM0
date	Date of the boundaries
validOn	Valid Date of the Boundaries
validTo	End of Valid Date of the Boundaries
SD_EN	Senatorial District
SD_PCODE	Unique Code of the Senatorial District
geometry	Polygon Data

Important

As NGA seems to offer a more richer data set the rest of the analysis will be done on the NGA Data set

Importing Aspatial Data

Loading the dataset from CSV

The next dataset that we will be loading would be the waterpoint dataset. As the dataset is found in the CSV another function read_csv(), which will import the csv as a tibble dataset. Read more about read_csv() from readr here.

Note

As the CSV contain almost 70 variables and more than 10000 observations it would be better to filter the dataset to the country of interest, in this case, Nigeria. Read more about filter() from dplyr here.

wp_nga <- read_csv("data/aspatial/WPdx.csv") %>%
  filter(`#clean_country_name` == "Nigeria")

Warning: One or more parsing issues, call `problems()` on your data frame for details,
e.g.:
  dat <- vroom(...)
  problems(dat)

Rows: 406566 Columns: 70
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (43): #source, #report_date, #status_id, #water_source_clean, #water_sou...
dbl (23): row_id, #lat_deg, #lon_deg, #install_year, #fecal_coliform_value, ...
lgl  (4): #rehab_year, #rehabilitator, is_urban, latest_record

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Converting the water point data into sf point feature.

Despite loading the aspatial dataframe into a tibble data frame, we would need to convert the dataframe into an sf data frame for us to perform Geospatial Analysis.

The column “New Georeferenced Column” contain the spatial data is a well-known text representation of geometry, as the such the fuction st_as_sfc() can be used to convert that into a sfc object. Read more about st_as_sfc() from sf here. We will append the sfc object into a new Column called “Geometry”.

wp_nga$Geometry = st_as_sfc(wp_nga$`New Georeferenced Column`)
wp_nga

# A tibble: 95,008 × 71
   row_id `#source`      #lat_…¹ #lon_…² #repo…³ #stat…⁴ #wate…⁵ #wate…⁶ #wate…⁷
    <dbl> <chr>            <dbl>   <dbl> <chr>   <chr>   <chr>   <chr>   <chr>  
 1 429068 GRID3             7.98    5.12 08/29/… Unknown <NA>    <NA>    Tapsta…
 2 222071 Federal Minis…    6.96    3.60 08/16/… Yes     Boreho… Well    Mechan…
 3 160612 WaterAid          6.49    7.93 12/04/… Yes     Boreho… Well    Hand P…
 4 160669 WaterAid          6.73    7.65 12/04/… Yes     Boreho… Well    <NA>   
 5 160642 WaterAid          6.78    7.66 12/04/… Yes     Boreho… Well    Hand P…
 6 160628 WaterAid          6.96    7.78 12/04/… Yes     Boreho… Well    Hand P…
 7 160632 WaterAid          7.02    7.84 12/04/… Yes     Boreho… Well    Hand P…
 8 642747 Living Water …    7.33    8.98 10/03/… Yes     Boreho… Well    Mechan…
 9 642456 Living Water …    7.17    9.11 10/03/… Yes     Boreho… Well    Hand P…
10 641347 Living Water …    7.20    9.22 03/28/… Yes     Boreho… Well    Hand P…
# … with 94,998 more rows, 62 more variables: `#water_tech_category` <chr>,
#   `#facility_type` <chr>, `#clean_country_name` <chr>, `#clean_adm1` <chr>,
#   `#clean_adm2` <chr>, `#clean_adm3` <chr>, `#clean_adm4` <chr>,
#   `#install_year` <dbl>, `#installer` <chr>, `#rehab_year` <lgl>,
#   `#rehabilitator` <lgl>, `#management_clean` <chr>, `#status_clean` <chr>,
#   `#pay` <chr>, `#fecal_coliform_presence` <chr>,
#   `#fecal_coliform_value` <dbl>, `#subjective_quality` <chr>, …

Now than we have a tibble data frame we would need to convert the data frame into a sf object using st_sf(). Read more about st_sf() here.

Important

It is important to note that the sfc object in the Geometry column does not contain the correct referencing system. There is a need to transform the projection into a WGS 84. The EPSG code is 4326.

wp_sf <- st_sf(wp_nga, crs=4326)
wp_sf

Simple feature collection with 95008 features and 70 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 2.707441 ymin: 4.301812 xmax: 14.21828 ymax: 13.86568
Geodetic CRS:  WGS 84
# A tibble: 95,008 × 71
   row_id `#source`      #lat_…¹ #lon_…² #repo…³ #stat…⁴ #wate…⁵ #wate…⁶ #wate…⁷
 *  <dbl> <chr>            <dbl>   <dbl> <chr>   <chr>   <chr>   <chr>   <chr>  
 1 429068 GRID3             7.98    5.12 08/29/… Unknown <NA>    <NA>    Tapsta…
 2 222071 Federal Minis…    6.96    3.60 08/16/… Yes     Boreho… Well    Mechan…
 3 160612 WaterAid          6.49    7.93 12/04/… Yes     Boreho… Well    Hand P…
 4 160669 WaterAid          6.73    7.65 12/04/… Yes     Boreho… Well    <NA>   
 5 160642 WaterAid          6.78    7.66 12/04/… Yes     Boreho… Well    Hand P…
 6 160628 WaterAid          6.96    7.78 12/04/… Yes     Boreho… Well    Hand P…
 7 160632 WaterAid          7.02    7.84 12/04/… Yes     Boreho… Well    Hand P…
 8 642747 Living Water …    7.33    8.98 10/03/… Yes     Boreho… Well    Mechan…
 9 642456 Living Water …    7.17    9.11 10/03/… Yes     Boreho… Well    Hand P…
10 641347 Living Water …    7.20    9.22 03/28/… Yes     Boreho… Well    Hand P…
# … with 94,998 more rows, 62 more variables: `#water_tech_category` <chr>,
#   `#facility_type` <chr>, `#clean_country_name` <chr>, `#clean_adm1` <chr>,
#   `#clean_adm2` <chr>, `#clean_adm3` <chr>, `#clean_adm4` <chr>,
#   `#install_year` <dbl>, `#installer` <chr>, `#rehab_year` <lgl>,
#   `#rehabilitator` <lgl>, `#management_clean` <chr>, `#status_clean` <chr>,
#   `#pay` <chr>, `#fecal_coliform_presence` <chr>,
#   `#fecal_coliform_value` <dbl>, `#subjective_quality` <chr>, …

Much like the Handling of the Geospatial data above, there is a need to conver the WGS84 projection to the projection coordinate system of Nigeria as well.

wp_sf <- wp_sf %>%
  st_transform(crs = 26392)

Geospatial Data Cleaning

At this step, we now know that we have already loaded all the dataset and that the next step of it would be cleaning the data.

Excluding Redundent Fields

Taking a look at the columns (NGA Data set (Humanitarian Data Exchange))of the NGA sf dataframe, we could identify most of the redundent fields. The only field that really matters would be the columns

Columns to Keep	Reasons
ADM2_EN	This is the English Name of the ADM2. This is where the Local Government Area.
ADM2_PCODE	This is the unique identifier of ADM2
ADM1_EN	This is the English Name of the ADM1. This is where the States of Nigeria is.
ADM1_PCODE	This is the unique identifier of ADM1

NGA <- NGA %>%
  select(c(3:4, 8:9))

Checking for Duplicate Name

We need to ensure that there is no duplicate name in the data. In this case, we only really care about checking for duplicate names in Local Government Area or ADM2. One method we can used to check for duplicated name would the used of the duplicated() function. Find out about the duplicated() from base R here.

NGA$ADM2_EN[duplicated(NGA$ADM2_EN)==TRUE]

[1] "Bassa"    "Ifelodun" "Irepodun" "Nasarawa" "Obi"      "Surulere"

Now that we know that there are similarities in the name we would need to examine the duplicate field more closely. One method we can used to check if the duplicated data are the same would be to take a look at their unique pcode.

NGA$ADM2_PCODE[duplicated(NGA$ADM2_PCODE)==TRUE]

character(0)

Now that we have establised that each of ADM2_PCODE is different, we can determined that the ADM2 names are the same but are referencing different area. In this case, there will be a need to correct the names of the ADM2_EN so that there will be no duplicate data.

Tip

A Google Search can be performed as well to double check they are indeed different area.

NGA$ADM2_EN[94] <- "Bassa, Kogi"
NGA$ADM2_EN[95] <- "Bassa, Plateau"
NGA$ADM2_EN[304] <- "Ifelodun, Kwara"
NGA$ADM2_EN[305] <- "Ifelodun, Osun"
NGA$ADM2_EN[355] <- "Irepodun, Kwara"
NGA$ADM2_EN[356] <- "Irepodun, Osun"
NGA$ADM2_EN[519] <- "Nasarawa, Kano"
NGA$ADM2_EN[520] <- "Nasarawa, Nasarawa"
NGA$ADM2_EN[546] <- "Obi, Benue"
NGA$ADM2_EN[547] <- "Obi, Nasarawa"
NGA$ADM2_EN[693] <- "Surulere, Lagos"
NGA$ADM2_EN[694] <- "Surulere, Oyo"

Now, we would need to confirm that the duplicated name issues has been addressed already.

NGA$ADM2_EN[duplicated(NGA$ADM2_EN)==TRUE]

character(0)

Data Wrangling for Water Point Data

Before we go about extracting the relevant details from the Water Point Data, we could perform some Exploratory Data Analysis to gain some initial understanding of the data.

Note

Note that we need to use the sf Dataframe for most of the analysis.

We can view the distribution of the water point through the use of freq() function of funModeling package. Find out about freq() from funModeling here.

freq(data = wp_sf,
     input = '#status_clean')

Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
of ggplot2 3.3.4.
ℹ The deprecated feature was likely used in the funModeling package.
  Please report the issue at <https://github.com/pablo14/funModeling/issues>.

                     #status_clean frequency percentage cumulative_perc
1                       Functional     45883      48.29           48.29
2                   Non-Functional     29385      30.93           79.22
3                             <NA>     10656      11.22           90.44
4      Functional but needs repair      4579       4.82           95.26
5 Non-Functional due to dry season      2403       2.53           97.79
6        Functional but not in use      1686       1.77           99.56
7         Abandoned/Decommissioned       234       0.25           99.81
8                        Abandoned       175       0.18           99.99
9 Non functional due to dry season         7       0.01          100.00

Let perform some analysis on the status of the water points. There seems to be 3 broad categories of the water point based on their status:

functional
non-functional
unknown.

However, some data wrangling task would need to be performed in order to make it easier to handle in subsequent steps

We would need to rename the “#status_clean” to “status_clean”. This is done through the use of rename() function from dplyr package. Find out more about rename() function from dplyr here.
After we have rename the column, we would need to select it into a new data frame. This is done through the use of select() function from dplyr package. Find out more about select() function from dplyr here.
Lastly, we would need replace all the NA value with “unknown”. this can be done through mutate() function and replace_na() function. Find out more about mutate() function here. Find out more about replace_na() function here.

wp_sf_nga <- wp_sf %>% 
  rename(status_clean = '#status_clean') %>%
  select(status_clean) %>%
  mutate(status_clean = replace_na(
    status_clean, "unknown"))

Extracting the Water Point Data

With some basic understanding of the water point, we can now categories the water point data. From the graph above we can categories it into the following method.

This is to extract functional water point
Waterpoint Category	Status
Functional	Functional
Functional	Functional but not in use
Functional	Functional but needs repair
Non Functional	Abandoned/Decommissioned
Non Functional	Abandoned
Non Functional	Non-Functional due to dry season
Non Functional	Non-Functional
Non Functional	Non functional due to dry season
Unknown	Unknown

wp_functional <- wp_sf_nga %>%
  filter(status_clean %in%
           c("Functional",
             "Functional but not in use",
             "Functional but needs repair"))

wp_functional

Simple feature collection with 52148 features and 1 field
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 29322.63 ymin: 33758.37 xmax: 1218553 ymax: 1092629
Projected CRS: Minna / Nigeria Mid Belt
# A tibble: 52,148 × 2
   status_clean            Geometry
 * <chr>                <POINT [m]>
 1 Functional   (128394.3 330487.9)
 2 Functional   (464684.4 94532.59)
 3 Functional   (588792.3 74102.03)
 4 Functional     (459153.3 171705)
 5 Functional   (586703.9 75701.92)
 6 Functional      (612461.7 87149)
 7 Functional     (503439 87320.23)
 8 Functional   (599467.7 92205.82)
 9 Functional   (651470.8 101586.9)
10 Functional   (650819.3 104796.9)
# … with 52,138 more rows

This is to extract nonfunctional water point.

wp_nonfunctional <- wp_sf_nga %>%
  filter(status_clean %in%
           c("Abandoned/Decommissioned",
             "Abandoned",
             "Non-Functional due to dry season",
             "Non-Functional",
             "Non functional due to dry season"))

wp_nonfunctional

Simple feature collection with 32204 features and 1 field
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 28907.91 ymin: 33736.93 xmax: 1209690 ymax: 1092883
Projected CRS: Minna / Nigeria Mid Belt
# A tibble: 32,204 × 2
   status_clean                        Geometry
 * <chr>                            <POINT [m]>
 1 Abandoned/Decommissioned (578642.2 141523.1)
 2 Abandoned/Decommissioned (571655.4 70856.98)
 3 Abandoned/Decommissioned   (571629.5 143544)
 4 Abandoned/Decommissioned (608748.8 141693.1)
 5 Abandoned/Decommissioned (576876.2 66860.76)
 6 Abandoned/Decommissioned   (698288 224655.8)
 7 Abandoned/Decommissioned (698293.1 224809.4)
 8 Abandoned/Decommissioned (341287.7 459644.6)
 9 Abandoned/Decommissioned (402193.2 89488.33)
10 Abandoned/Decommissioned (589410.8 147917.3)
# … with 32,194 more rows

This is to extract unknown water point

wp_unknown <- wp_sf_nga %>%
  filter(status_clean == "unknown")

wp_unknown

Simple feature collection with 10656 features and 1 field
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 29143.21 ymin: 36660.5 xmax: 1293293 ymax: 965811.9
Projected CRS: Minna / Nigeria Mid Belt
# A tibble: 10,656 × 2
   status_clean            Geometry
 * <chr>                <POINT [m]>
 1 unknown      (297874.6 441473.8)
 2 unknown      (607559.4 274905.5)
 3 unknown      (576523.1 301556.6)
 4 unknown      (578321.7 307339.8)
 5 unknown      (590994.2 326738.8)
 6 unknown      (597909.2 333608.5)
 7 unknown      (724171.9 367609.1)
 8 unknown      (737994.1 350616.5)
 9 unknown      (749790.1 354304.6)
10 unknown      (728109.9 367079.1)
# … with 10,646 more rows

EDA on waterpoints

Now that we have extracted the water point data, we can have a better look at water points from each category.

This is for Functional Water point

freq(data = wp_functional,
     input = 'status_clean')

                 status_clean frequency percentage cumulative_perc
1                  Functional     45883      87.99           87.99
2 Functional but needs repair      4579       8.78           96.77
3   Functional but not in use      1686       3.23          100.00

This is for Non Functional Water Point

freq(data = wp_nonfunctional,
     input = 'status_clean')

                      status_clean frequency percentage cumulative_perc
1                   Non-Functional     29385      91.25           91.25
2 Non-Functional due to dry season      2403       7.46           98.71
3         Abandoned/Decommissioned       234       0.73           99.44
4                        Abandoned       175       0.54           99.98
5 Non functional due to dry season         7       0.02          100.00

This is Unknown Water Point

freq(data = wp_unknown,
     input = 'status_clean')

  status_clean frequency percentage cumulative_perc
1      unknown     10656        100             100

Performing Point In Polygon Count.

While knowing the number of total functional and nonfunctional and unknown water point is important, it would be better if we are able to see the status of each water point in each of the LGA.

To do that we would need to perform a series of steps.

We would need to make use of the st_intersects() function of sf package to identify the functional water points in each LGA. Find out more about st_intersects() function of sf package here
We would need to make use of lengths() function from base r to calculate the number of functional water points that fall inside each LGA. Find out more about lengths() function of base r here.

All of this is added to a new sf data frame “NGA_wp” to be used in subsequent steps.

NGA_wp <- NGA %>% 
  mutate(`total_wp` = lengths(
    st_intersects(NGA, wp_sf_nga))) %>%
  mutate(`wp_functional` = lengths(
    st_intersects(NGA, wp_functional))) %>%
  mutate(`wp_nonfunctional` = lengths(
    st_intersects(NGA, wp_nonfunctional))) %>%
  mutate(`wp_unknown` = lengths(
    st_intersects(NGA, wp_unknown)))

Visualising Attributes

Now that we have the point in polygon count we can reveal the distribution of the waterpoint.

We can make use of the ggplot2 packages to help plot. ggplot2 is part of tidyverse, and more information can be found here.

Distribution of Total Water point

ggplot(data = NGA_wp,
       aes(x = wp_functional)) + 
  geom_histogram(bins=20,
                 color="black",
                 fill="light blue") +
  geom_vline(aes(xintercept=mean(
    total_wp, na.rm=T)),
             color="red", 
             linetype="dashed", 
             size=0.8) +
  ggtitle("Distribution of total water points by LGA") +
  xlab("No. of water points") +
  ylab("No. of\nLGAs") +
  theme(axis.title.y=element_text(angle = 0))

Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.

Distribution of Functional Water point

ggplot(data = NGA_wp,
       aes(x = wp_nonfunctional)) + 
  geom_histogram(bins=20,
                 color="black",
                 fill="light blue") +
  geom_vline(aes(xintercept=mean(
    total_wp, na.rm=T)),
             color="red", 
             linetype="dashed", 
             size=0.8) +
  ggtitle("Distribution of total water points by LGA") +
  xlab("No. of water points") +
  ylab("No. of\nLGAs") +
  theme(axis.title.y=element_text(angle = 0))

Distribution of Non Functional Water point

ggplot(data = NGA_wp,
       aes(x = total_wp)) + 
  geom_histogram(bins=20,
                 color="black",
                 fill="light blue") +
  geom_vline(aes(xintercept=mean(
    total_wp, na.rm=T)),
             color="red", 
             linetype="dashed", 
             size=0.8) +
  ggtitle("Distribution of total water points by LGA") +
  xlab("No. of water points") +
  ylab("No. of\nLGAs") +
  theme(axis.title.y=element_text(angle = 0))

Distribution of Unknown Water point

ggplot(data = NGA_wp,
       aes(x = wp_unknown)) + 
  geom_histogram(bins=20,
                 color="black",
                 fill="light blue") +
  geom_vline(aes(xintercept=mean(
    total_wp, na.rm=T)),
             color="red", 
             linetype="dashed", 
             size=0.8) +
  ggtitle("Distribution of total water points by LGA") +
  xlab("No. of water points") +
  ylab("No. of\nLGAs") +
  theme(axis.title.y=element_text(angle = 0))

Saving the Data into RDS format

Now that we have done all the above work in order to get sf object structure for us to perform geospatial analytics, it would be a shame if all the hardwork is gone. As such, it is important that we save the data into rds format.

We can make use of the write_rds() function from readr package to export the sf dataframe into a rds format. Find out more about write_rds() function from readr package here.

Note

RDS format is a R native data format, which allows for R object to be save for later used.

write_rds(NGA_wp, "data/rds/NGA_wp.rds")

Mapping the Functional and Non Functional Points

tmap_mode("view")

tmap mode set to interactive viewing

tm_shape(NGA) +
  tm_polygons() +
tm_shape(wp_functional)+ 
  tm_dots(col = "status_clean",
             size = 0.01,
             border.col = "black",
             border.lwd = 0.5,
          palette = "blue") + 
  tm_shape(wp_nonfunctional)+ 
  tm_dots(col = "status_clean",
             size = 0.01,
             border.col = "black",
             border.lwd = 0.5,
          palette = "red") +
  tm_view(set.zoom.limits = c(6, 10))

tmap_mode("plot")

tmap mode set to plotting

tm_shape(NGA) +
  tm_borders(col = "grey40", lwd = 1, lty = "solid")+
tm_shape(wp_functional)+
  tm_dots(legend.show = TRUE, col = "blue") +
  tm_shape(wp_nonfunctional) +
  tm_dots(legend.show = TRUE, col = "red")

Geospatial Data Wrangling

Converting sf data to sp’s Spatial Class

” This is just a placeholder text”

wp_functional_spatial <- as_Spatial(wp_functional)
wp_nonfunctional_spatial <- as_Spatial(wp_nonfunctional)
NGA_spatial <- as_Spatial(NGA)

Viewing each of the sp Spatial Class

Functional

wp_functional_spatial

class       : SpatialPointsDataFrame 
features    : 52148 
extent      : 29322.63, 1218553, 33758.37, 1092629  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs 
variables   : 1
names       :              status_clean 
min values  :                Functional 
max values  : Functional but not in use

Non Functional

wp_nonfunctional_spatial

class       : SpatialPointsDataFrame 
features    : 32204 
extent      : 28907.91, 1209690, 33736.93, 1092883  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs 
variables   : 1
names       :                     status_clean 
min values  :                        Abandoned 
max values  : Non functional due to dry season

NGA

NGA_spatial

class       : SpatialPolygonsDataFrame 
features    : 774 
extent      : 26662.71, 1344157, 30523.38, 1096029  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs 
variables   : 4
names       :   ADM2_EN, ADM2_PCODE, ADM1_EN, ADM1_PCODE 
min values  : Aba North,   NG001001,    Abia,      NG001 
max values  :      Zuru,   NG037014, Zamfara,      NG037

Converting the Spatial Class into generic sp format

wp_functional_sp <- as(wp_functional_spatial, "SpatialPoints")
wp_nonfunctional_sp <- as(wp_nonfunctional_spatial, "SpatialPoints")
NGA_sp <- as(NGA_spatial, "SpatialPolygons")

Viewing each

wp_functional_sp

class       : SpatialPoints 
features    : 52148 
extent      : 29322.63, 1218553, 33758.37, 1092629  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs

wp_nonfunctional_sp

class       : SpatialPoints 
features    : 32204 
extent      : 28907.91, 1209690, 33736.93, 1092883  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs

NGA_sp

class       : SpatialPolygons 
features    : 774 
extent      : 26662.71, 1344157, 30523.38, 1096029  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs

Converting into spatstas ppp format

wp_functional_ppp <- as(wp_functional_sp , "ppp")
wp_nonfunctional_ppp <- as(wp_nonfunctional_sp , "ppp")

wp_functional_ppp

Planar point pattern: 52148 points
window: rectangle = [29322.6, 1218553.3] x [33758.4, 1092628.9] units

wp_nonfunctional_ppp

Planar point pattern: 32204 points
window: rectangle = [28907.9, 1209690] x [33736.9, 1092882.6] units

Checking for Duplicate Points

any(duplicated(wp_functional_ppp))

[1] FALSE

any(duplicated(wp_nonfunctional_ppp))

[1] FALSE

Creating Owin Object

NGA_owin <- as(NGA_sp, "owin")

plot(NGA_owin)

Combining Non Functional Water Point and Functional Water Point with Owin

wp_functional_NGA_ppp = wp_functional_ppp[NGA_owin]

wp_nonfunctional_NGA_ppp = wp_nonfunctional_ppp[NGA_owin]

plot(wp_functional_NGA_ppp)

plot(wp_nonfunctional_NGA_ppp)

Kernel density Estimation

Rescaling the KDE values

wp_functional_NGA_ppp.km <- rescale(wp_functional_NGA_ppp, 1000, "km")
wp_nonfunctional_NGA_ppp.km <- rescale(wp_nonfunctional_NGA_ppp, 1000, "km")

Plotting the Kernal Density

wp_functional_NGA.bw <- density(wp_functional_NGA_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(wp_functional_NGA.bw)

wp_nonfunctional_NGA.bw <- density(wp_nonfunctional_NGA_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(wp_nonfunctional_NGA.bw)

Converting to Grid Object

gridded_kde_wp_nonfunctional_NG_bw <- as.SpatialGridDataFrame.im(wp_nonfunctional_NGA.bw)
spplot(gridded_kde_wp_nonfunctional_NG_bw)

gridded_kde_wp_functional_NG_bw <- as.SpatialGridDataFrame.im(wp_functional_NGA.bw)
spplot(gridded_kde_wp_functional_NG_bw)

Converting to Raster

kde_wp_functional_NG_bw_raster <- raster(gridded_kde_wp_functional_NG_bw)
kde_wp_nonfunctional_NG_raster <- raster(gridded_kde_wp_nonfunctional_NG_bw)

projection(kde_wp_functional_NG_bw_raster) <- CRS("+init=EPSG:26392")
projection(kde_wp_nonfunctional_NG_raster) <- CRS("+init=EPSG:26392")

kde_wp_functional_NG_bw_raster

class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 10.29292, 8.324266  (x, y)
extent     : 26.66271, 1344.157, 30.52338, 1096.029  (xmin, xmax, ymin, ymax)
crs        : +init=EPSG:26392 
source     : memory
names      : v 
values     : -4.383912e-16, 4.843545  (min, max)

kde_wp_nonfunctional_NG_raster

class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 10.29292, 8.324266  (x, y)
extent     : 26.66271, 1344.157, 30.52338, 1096.029  (xmin, xmax, ymin, ymax)
crs        : +init=EPSG:26392 
source     : memory
names      : v 
values     : -2.410108e-16, 1.517255  (min, max)

Plotting Kernal density Map of Whole Nigeria

tm_shape(kde_wp_functional_NG_bw_raster) + 
    tm_layout(main.title = "Kernal Density Map of Functional Water Point of Nigeria") +
  tm_raster("v" , midpoint = NA) +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)

tm_shape(kde_wp_nonfunctional_NG_raster) + 
    tm_layout(main.title = "Kernal Density Map of Non Functional Water Point of Nigeria") +
  tm_raster("v" , midpoint = NA) +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)

Plotting Kernal Density Map of Osun Area

Extracting Osun State from NGA

osun = NGA_spatial[NGA_spatial@data$ADM1_EN == "Osun",]

plot(osun)

osun_sp = as(osun, "SpatialPolygons")

osun_owin = as(osun_sp, "owin")

wp_functional_osun_ppp = wp_functional_ppp[osun_owin]
wp_nonfunctional_osun_ppp = wp_nonfunctional_ppp[osun_owin]

wp_functional_osun_ppp.km = rescale(wp_functional_osun_ppp, 1000, "km")
wp_nonfunctional_osun_ppp.km = rescale(wp_nonfunctional_osun_ppp, 1000, "km")

plot(wp_functional_osun_ppp.km)

wp_nonfunctional_osun.bw <- density(wp_nonfunctional_osun_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(wp_nonfunctional_osun.bw)

wp_functional_osun.bw <- density(wp_functional_osun_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(wp_functional_osun.bw)

gridded_kde_wp_functional_osun_bw <- as.SpatialGridDataFrame.im(wp_functional_osun.bw)
spplot(gridded_kde_wp_functional_osun_bw)

gridded_kde_wp_nonfunctional_osun_bw <- as.SpatialGridDataFrame.im(wp_nonfunctional_osun.bw)
spplot(gridded_kde_wp_nonfunctional_osun_bw)

kde_wp_functional_osun_bw_raster <- raster(gridded_kde_wp_functional_osun_bw)
kde_wp_nonfunctional_osun_bw_raster <- raster(gridded_kde_wp_nonfunctional_osun_bw)

projection(kde_wp_functional_osun_bw_raster) <- CRS("+init=EPSG:26393")
projection(kde_wp_nonfunctional_osun_bw_raster) <- CRS("+init=EPSG:26393")

kde_wp_functional_osun_bw_raster

class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.8948485, 0.9616045  (x, y)
extent     : 176.5032, 291.0438, 331.4347, 454.5201  (xmin, xmax, ymin, ymax)
crs        : +init=EPSG:26393 
source     : memory
names      : v 
values     : -4.876249e-15, 25.49435  (min, max)

tm_shape(kde_wp_functional_osun_bw_raster) + 
    tm_layout(main.title = "Kernal Density Map of Functional Water Point of Nigeria") +
  tm_raster("v") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)

Variable(s) "v" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

tm_shape(kde_wp_nonfunctional_osun_bw_raster) + 
    tm_layout(main.title = "Kernal Density Map of Non Functional Water Point of Nigeria") +
  tm_raster("v") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)

Variable(s) "v" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

Analysis of Kernal Density Points

Testing for Distribution Clarks and Evens

The test hypotheses are:

Ho = The distribution of water points are randomly distributed.

H1= The distribution of water points are not randomly distributed.

The 95% confident interval will be used.

clarkevans.test(wp_functional_osun_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"),
                nsim=99)


    Clark-Evans test
    No edge correction
    Monte Carlo test based on 99 simulations of CSR with fixed n

data:  wp_functional_osun_ppp
R = 0.44767, p-value = 0.01
alternative hypothesis: clustered (R < 1)

Note

We therefore reject the null Hypothesis that the Functional water point are randomly distributed.

clarkevans.test(wp_nonfunctional_osun_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"),
                nsim=99)


    Clark-Evans test
    No edge correction
    Monte Carlo test based on 99 simulations of CSR with fixed n

data:  wp_nonfunctional_osun_ppp
R = 0.44327, p-value = 0.01
alternative hypothesis: clustered (R < 1)

Note

We therefore reject the null Hypothesis that the non Functional water point are randomly distributed.

Analysis of Functional and Non Functional Water point

When looking at the 2 Kernal Density Points, it is easy to assume that there seems to be almost no pattern on the density of the water point, however, one can easily assume that there is no pattern in where all the water points are located. However upon further inspection, there seems to be 2 trends that can be spotted based in the difference in map density.

Areas with High Functional Water Point and Non Functional Water Point seems to be located in cities.

Taking a look at the map above and comparing it with the KDE Map, areas with high density of functional and non functional water points seems to coincide with where the major cities are located. This seems to make the most sense as cities are where most people lives and need the access to water, as such it make sense most of the water point to concentrate itself in the cities. In This regards, Large Cities tend to have a larger concentration of functional and non functional water points as compared to smaller cities.

Ede seems to have the largest amount of Functional Water Point, whereas Ife seems to have the largest amount of Non Functional Water Point.

In Cities with High Density of Functional Water Point, the Density of Non Functional Water Point is Low relatively.

Tip

Density of Water points are taken in context among the cities

As we have already establish that water points are concentrated at cities, it would make sense that most of our Analysis will focus upon the cities. In this regard, one surprising fact is that cities with High Density of Functional Water Point tend to have a comparitively lower density of Functional Water point. Take Ede for example, it has the highest density of Functional Water Point, yet it has one of the lower level of Non Functional Water Points relatively. This trend can be seen in Ife and other areas as well.

However, there seems to be one exception to this trend, and that would be the city of Iwo. The city Iwo observed a high density of both functional and non functional water points.

Comparison between Kernal Density Map and Point Map.

Kernal Density Map are better at spotting trends as compared to Point Map

Kernal Density Map are much better at spotting trends as compared to that of the point map. A Point map will highlight each individual water point out and this can be difficult for us to determine any trend at all. With reference to the map in Mapping the Functional and Non Functional Points, there seems to be almost no difference in the density of the water points in the area, or at the very least it is difficult to tell. A Kernal Density Map solve this by smoothing over the points and providing a density number.

Kernal Density Map are less computationally intensive to display as compared to Point Map

A Point Map with it thousands of points is more computationally intensive to display are compared to Kernal Density Map. This is because the computer would need to take note of every individual point and plot it out which would be an issue for computers with low computational power.

Spatial Correlation Analysis

Now that we have analysed the spatial point patters, we would need to confirm our observations statistically - which is where hypothesis comes in.

H0: The distribution of the Functional Water Points Listings are randomly distributed
H1: The distribution of the Non Functional Water Points are not randomly distributed
Confidence level : 99%

We will be performing the Hypothesis Testing for 3 different cities that I have selected and that would be the Osogbo, Ede and Iwo.

Defining the Areas

iwo = NGA_spatial[NGA_spatial@data$ADM2_EN == "Iwo",] 
osogbo = NGA_spatial[NGA_spatial@data$ADM2_EN == "Osogbo",]
ede = NGA_spatial[NGA_spatial@data$ADM2_EN %in% c("Ede North","Ede South"),]

iwo_sp = as(iwo, "SpatialPolygons")
osogbo_sp = as(osogbo, "SpatialPolygons")
ede_sp = as(ede, "SpatialPolygons")

iwo_owin = as(iwo, "owin")
osogbo_owin = as(osogbo, "owin")
ede_owin = as(ede, "owin")

wp_functional_iwo_ppp = wp_functional_ppp[iwo_owin]
wp_nonfunctional_iwo_ppp = wp_nonfunctional_ppp[iwo_owin]

wp_functional_osogbo_ppp = wp_functional_ppp[osogbo_owin]
wp_nonfunctional_osogbo_ppp = wp_nonfunctional_ppp[osogbo_owin]

wp_functional_ede_ppp = wp_functional_ppp[ede_owin]
wp_nonfunctional_ede_ppp = wp_nonfunctional_ppp[ede_owin]

wp_functional_iwo_ppp.km = rescale(wp_functional_iwo_ppp, 1000, "km")
wp_nonfunctional_iwo_ppp.km = rescale(wp_nonfunctional_iwo_ppp, 1000, "km")

wp_functional_osogbo_ppp.km = rescale(wp_functional_osogbo_ppp, 1000, "km")
wp_nonfunctional_osogbo_ppp.km = rescale(wp_nonfunctional_osogbo_ppp, 1000, "km")

wp_functional_ede_ppp.km = rescale(wp_functional_ede_ppp, 1000, "km")
wp_nonfunctional_ede_ppp.km = rescale(wp_nonfunctional_ede_ppp, 1000, "km")

Computing G Score

Iwo

Functional Water Point

H0: The distribution of the Functional Water Points in Iwo are randomly distributed
H1: The distribution of the Functional Water Points in Iwo are not randomly distributed
Confidence level : 99%
Significance level : 0.01
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.01.

G_iwo_fuctional.csr <- envelope(wp_functional_iwo_ppp.km, Gest, nsim=100)

Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.

plot(G_iwo_fuctional.csr)

Conclusion: The observed G(r) is far above the G(theo) as well as the envelope - indicating that Functional Water Point in the Iwo area are clustered. Hence, we reject the null hypothesis that Functional Water Point in the Iwo area are randomly distributed at 99% confident interval.

Non Functional Water Point

H0: The distribution of the Non Functional Water Points in Iwo are randomly distributed
H1: The distribution of the Non Functional Water Points in Iwo are not randomly distributed
Confidence level : 99%
Significance level : 0.01
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.01.

G_iwo_nonfuctional.csr <- envelope(wp_nonfunctional_iwo_ppp.km, Gest, nsim=100)

Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.

plot(G_iwo_nonfuctional.csr)

Conclusion: The observed G(r) is far above the G(theo) as well as the envelope - indicating that Non Functional Water Point in the Iwo area are clustered. Hence, we reject the null hypothesis that Non Functional Water Point in the Iwo area are randomly distributed at 99% confident interval.

Osogbo

Functional Water Point

H0: The distribution of the Functional Water Points in Osogbo are randomly distributed
H1: The distribution of the Functional Water Points in Osogbo are not randomly distributed
Confidence level : 99%
Significance level : 0.01
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.01.

G_osogbo_fuctional.csr <- envelope(wp_functional_osogbo_ppp.km, Gest, nsim=100)

Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.

plot(G_osogbo_fuctional.csr)

Conclusion: The observed G(r) is far above the G(theo) as well as the envelope - indicating that Functional Water Point in the Osogbo area are clustered. Hence, we reject the null hypothesis that Functional Water Point in the Osogbo area are randomly distributed at 99% confident interval.

Non Functional Water Point

H0: The distribution of the Non Functional Water Points in Osogbo are randomly distributed
H1: The distribution of the Non Functional Water Points in Osogbo are not randomly distributed
Confidence level : 99%
Significance level : 0.01
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.01.

G_osogbo_nonfuctional.csr <- envelope(wp_nonfunctional_osogbo_ppp.km, Gest, nsim=100)

Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.

plot(G_osogbo_nonfuctional.csr)

Conclusion: The observed G(r) is far above the G(theo) as well as the envelope - indicating that Non Functional Water Point in the Osobo area are clustered. Hence, we reject the null hypothesis that Non Functional Water Point in the Osobo area are randomly distributed at 99% confident interval.

Ede

Functional Water Point

H0: The distribution of the Functional Water Points in Ede are randomly distributed
H1: The distribution of the Functional Water Points in Ede are not randomly distributed
Confidence level : 99%
Significance level : 0.01
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.01.

G_ede_fuctional.csr <- envelope(wp_functional_ede_ppp.km, Gest, nsim=100)

Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.

plot(G_ede_fuctional.csr)

Conclusion: The observed G(r) is far above the G(theo) as well as the envelope - indicating that Functional Water Point in the Ede area are clustered. Hence, we reject the null hypothesis that Functional Water Point in the Ede area are randomly distributed at 99% confident interval.

Non Functional Water Point

H0: The distribution of the Non Functional Water Points in Ede are randomly distributed
H1: The distribution of the Non Functional Water Points in Ede are not randomly distributed
Confidence level : 99%
Significance level : 0.01
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.01.

G_ede_nonfuctional.csr <- envelope(wp_nonfunctional_ede_ppp.km, Gest, nsim=100)

Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.

plot(G_ede_nonfuctional.csr)

Conclusion: The observed G(r) is far above the G(theo) as well as the envelope - indicating that Non Functional Water Point in the Ede area are clustered. Hence, we reject the null hypothesis that Non Functional Water Point in the Ede area are randomly distributed at 99% confident interval.

Osun

Functional Water Point

H0: The distribution of the Functional Water Points in Osun are randomly distributed
H1: The distribution of the Functional Water Points in Osun are not randomly distributed
Confidence level : 99%
Significance level : 0.01
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.01.

G_osun_fuctional.csr <- envelope(wp_functional_osun_ppp.km, Gest, nsim=100)

Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.

plot(G_osun_fuctional.csr)

Conclusion: The observed G(r) is far above the G(theo) as well as the envelope - indicating that Functional Water Point in the Osun area are clustered. Hence, we reject the null hypothesis that Functional Water Point in the Osun area are randomly distributed at 99% confident interval.

Non Functional Water Point

H0: The distribution of the Non Functional Water Points in Ede are randomly distributed
H1: The distribution of the Non Functional Water Points in Ede are not randomly distributed
Confidence level : 99%
Significance level : 0.01
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.01.

G_osun_nonfuctional.csr <- envelope(wp_nonfunctional_osun_ppp.km, Gest, nsim=100)

Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.

plot(G_osun_nonfuctional.csr)

Conclusion: The observed G(r) is far above the G(theo) as well as the envelope - indicating that Non Functional Water Point in the Osun area are clustered. Hence, we reject the null hypothesis that Functional Water Point in the Osun area are randomly distributed at 99% confident interval.